Power units and conversions One kilowatt (kW) equals which of the following in base S.I. units?

Introduction / Context:
Power quantifies the rate at which work is done or energy is transferred. The S.I. unit of power is the watt (W), defined as one joule per second. Kilowatt is a common multiple used in electrical and mechanical engineering. This question checks your ability to convert between kW and the fundamental S.I. units newton, metre, and second.

Given Data / Assumptions:

• 1 W = 1 J/s.
• 1 J = 1 N·m.
• 1 kW = 1000 W.

Concept / Approach:
Combine the definitions systematically. Since 1 W = 1 J/s and 1 J = 1 N·m, it follows that 1 W = 1 N·m/s. Therefore, multiplying by 1000 gives 1 kW = 1000 N·m/s. This representation is universally valid for mechanical and electrical power, independent of the conversion path.

Step-by-Step Solution:
Start: 1 W = 1 J/s.Use: 1 J = 1 N·m → 1 W = 1 N·m/s.Scale: 1 kW = 1000 W → 1000 N·m/s.Thus, select 1000 N·m/s as the correct equivalence.

Verification / Alternative check:
Electrical: P = V * I; 1 kW could be 1000 W at 250 V and 4 A, yet in base units the rate of energy transfer is still 1000 J every second, i.e., 1000 N·m/s.

Why Other Options Are Wrong:

• 1 N·m/s is 1 W, not 1 kW.
• 100 N·m is work/energy, not power (missing per-second).
• 1 × 10^6 N·m/s corresponds to 1 MW, not 1 kW.
• 1000 J is energy, not a rate.

Common Pitfalls:
Confusing energy (joule) with power (joule per second). Always check dimensions include time in the denominator for power.

Final Answer:
1000 N·m/s